Dynamic earthquake sequence simulation with a SBIEM without periodic boundaries

Dynamic earthquake sequence simulation is an important tool for investigating the behavior of a fault that hosts a series of earthquakes because it solves all interrelated stages in the earthquake cycle consistently, including nucleation, propagation and arrest of dynamic rupture, afterslip, locking, and interseismic stress accumulation. Numerically simulating and resolving these phenomena, which have different time and length scales, in a single framework is challenging. A spectral boundary integral equation method (SBIEM) that makes use of a fast Fourier transform is widely used because it reduces required computational costs, even though it can only be used for a planar fault. The conventional SBIEM has a periodic boundary condition as a result of the discretization of the wavenumber domain with a regular mesh; thus, to obtain an approximate solution for a fault in an infinite medium, it has been necessary to simulate a region much longer than the source distribution. Here, I propose a new SBIEM that is free from this artificial periodic boundary condition. In the proposed method, the periodic boundaries are removed by using a previously proposed method for the simulation of dynamic rupture. The integration kernel for the elastostatic effect, which reaches infinitely far from the source, is expressed analytically and replaces the one in the conventional SBIEM. The new method requires simulation of a region only twice as long as the source distribution, so the computational costs are significantly less than those required by the conventional SBIEM to simulate a fault in an infinite medium. The effect of the distance λ between the artificial periodic boundaries was investigated by comparing solutions for a typical problem setting between the conventional and proposed SBIEM. The result showed that the artificial periodic boundaries cause overestimation of the recurrence interval that is proportional to λ⁻². If λ is four times the fault length, the interval is overestimated by less than 1%. Thus, the artificial periodic boundaries have only a modest effect on the conclusions of previous studies.